The implementation of slab geometry for membrane-channel molecular dynamics simulations

Correlations in Charged Multipore Systems: Implications for Enhancing Selectivity and Permeability in Nanoporous Membranes

Nanoporous membranes have emerged as powerful tools for diverse applications, including gas separation and water desalination. Achieving high permeability for desired molecules alongside exceptional rejection of other species presents a significant design challenge. One potential strategy involves optimizing the chemistry and geometry of isolated nanopores to enhance permeability and selectivity while maximizing their density within a membrane. However, the impact of the pore proximity on membrane performance remains an open question. Through path sampling simulations of model graphitic membranes with multiple subnanometer pores, we reveal that nanoscale proximity between pores detrimentally affects water permeability and salt rejection. Specifically, counterion transport is decelerated, while co-ion transport is accelerated, due to direct interactions among water molecules, salt ions, and the dipoles within neighboring pores. Notably, the observed ionic transport time scales significantly deviate from established theories such as the access resistance model but are well explained using the simple phenomenological model that we develop in this work. We use this model to prescreen and optimize pore arrangements that elicit minimal correlations at a target pore density. These findings deepen our understanding of multipore systems, informing the rational design of nanoporous membranes for enhanced separation processes such as water desalination. They also shed light on the physiology of biological cells that employ ion channel proteins to modulate ion transport and reversal potentials.

Ideal conductor/dielectric model (ICDM): A generalized technique to correct for finite-size effects in molecular simulations of hindered ion transport

Molecular simulations serve as indispensable tools for investigating the kinetics and elucidating the mechanism of hindered ion transport across nanoporous membranes. In particular, recent advancements in advanced sampling techniques have made it possible to access translocation timescales spanning several orders of magnitude. In our prior study [Shoemaker et al., J. Chem. Theory Comput. 18, 7142 (2022)], we identified significant finite size artifacts in simulations of pressure-driven hindered ion transport through nanoporous graphitic membranes. We introduced the ideal conductor model, which effectively corrects for such artifacts by assuming the feed to be an ideal conductor. In the present work, we introduce the ideal conductor dielectric model (Icdm), a generalization of our earlier model, which accounts for the dielectric properties of both the membrane and the filtrate. Using the Icdm model substantially enhances the agreement among corrected free energy profiles obtained from systems of varying sizes, with notable improvements observed in regions proximate to the pore exit. Moreover, the model has the capability to consider secondary ion passage events, including the transport of a co-ion subsequent to the traversal of a counter-ion, a feature that is absent in our original model. We also investigate the sensitivity of the new model to various implementation details. The Icdm model offers a universally applicable framework for addressing finite size artifacts in molecular simulations of ion transport. It stands as a significant advancement in our quest to use molecular simulations to comprehensively understand and manipulate ion transport processes through nanoporous membranes.

Computer Simulation Insight into the Adsorption and Diffusion of Polyelectrolytes on Oppositely Charged Surface

In the present work, by means of computer simulation, we studied the adsorption and diffusion of polyelectrolyte macromolecules on oppositely charged surfaces. We considered the surface coverage and the charge of the adsorbed layer depending on the ionization degree of the macromolecules and the charge of the surface and carried out a computer experiment on the polymer diffusion within the adsorbed layers, taking into account its strong dependency on the surface coverage and the macromolecular ionization degree. The different regimes were distinguished that provided maximal mobility of the polymer chains along with a high number of charged groups in the layer, which could be beneficial for the development of the functional coatings. The results were compared with those of previous experiments on the adsorption of polyelectrolyte layers that may be applied as biocidal renewable coatings that can reversibly desorb from the surface.

Lamellarity-Driven Differences in Surface Structural Features of DPPS Lipids: Spectroscopic, Calorimetric and Computational Study

Although single-lipid bilayers are usually considered models of eukaryotic plasma membranes, their research drops drastically when it comes to exclusively anionic lipid membranes. Being a major anionic phospholipid in the inner leaflet of eukaryote membranes, phosphatidylserine-constituted lipid membranes were occasionally explored in the form of multilamellar liposomes (MLV), but their inherent instability caused a serious lack of efforts undertaken on large unilamellar liposomes (LUVs) as more realistic model membrane systems. In order to compensate the existing shortcomings, we performed a comprehensive calorimetric, spectroscopic and MD simulation study of time-varying structural features of LUV made from 1,2-dipalmitoyl-sn-glycero-3-phospho-L-serine (DPPS), whereas the corresponding MLV were examined as a reference. A substantial uncertainty of UV/Vis data of LUV from which only T_m was unambiguously determined (53.9 ± 0.8 °C), along with rather high uncertainty on the high-temperature range of DPPS melting profile obtained from DSC (≈50-59 °C), presumably reflect distinguished surface structural features in LUV. The FTIR signatures of glycerol moiety and those originated from carboxyl group serve as a strong support that in LUV, unlike in MLV, highly curved surfaces occur continuously, whereas the details on the attenuation of surface features in MLV were unraveled by molecular dynamics.

Ideal Conductor Model: An Analytical Finite-Size Correction for Nonequilibrium Molecular Dynamics Simulations of Ion Transport through Nanoporous Membranes

Modulating ion transport through nanoporous membranes is critical to many important chemical and biological separation processes. The corresponding transport timescales, however, are often too long to capture accurately using conventional molecular dynamics (MD). Recently, path sampling techniques, such as forward-flux sampling (FFS), have emerged as attractive alternatives for efficiently and accurately estimating arbitrarily long ionic passage times. Here, we use non-equilibrium MD and FFS to explore how the kinetics and mechanisms of pressure-driven chloride transport through a nanoporous graphitic membrane are affected by its lateral dimensions. We not only find ionic passage times and free energy barriers to decrease dramatically upon increasing the membrane surface area but also observe an abrupt and discontinuous change in the locus of the transition state. These strong finite size effects arise due to the cumulative effect of the periodic images of the leading ion entering the pore on the distribution of the induced excess charge at the membrane surface in the feed. By assuming that the feed is an ideal conductor, we analytically derive a finite size correction term that can be computed from the information obtained from a single simulation and successfully use it to obtain corrected free energy profiles with no dependence on the system size. We then estimate ionic passage times in the thermodynamic limit by assuming an Eyring-type dependence of rates on barriers with a size-independent prefactor. This approach constitutes a universal framework for removing finite size artifacts in molecular simulations of ion transport through nanoporous membranes and biological channel proteins.

The Effects of Cholesterol Oxidation on Erythrocyte Plasma Membranes: A Monolayer Study

Cholesterol plays a key role in the molecular and mesoscopic organisation of lipid membranes and it is expected that changes in its molecular structure (e.g., through environmental factors such as oxidative stress) may affect adversely membrane properties and function. In this study, we present evidence that oxidation of cholesterol has significant effects on the mechanical properties, molecular and mesoscopic organisation and lipid-sterol interactions in condensed monolayers composed of the main species found in the inner leaflet of the erythrocyte membrane. Using a combination of experimental methods (static area compressibility, surface dilatational rheology, fluorescence microscopy, and surface sensitive X-ray techniques) and atomistic molecular dynamics simulations, we show that oxidation of cholesterol to 7-ketocholesterol leads to stiffening of the monolayer (under both static and dynamic conditions), significant changes in the monolayer microdomain organisation, disruption in the van der Waals, electrostatic and hydrophobic interactions between the sterol and the other lipid species, and the lipid membrane hydration. Surface sensitive X-ray techniques reveal that, whilst the molecular packing mode is not significantly affected by cholesterol oxidation in these condensed phases, there are subtle changes in membrane thickness and a significant decrease in the coherence length in monolayers containing 7-ketocholesterol.

The role of structural order in heterogeneous ice nucleation

The freezing of water into ice is a key process that is still not fully understood. It generally requires an impurity of some description to initiate the heterogeneous nucleation of the ice crystals. The molecular structure, as well as the extent of structural order within the impurity in question, both play an essential role in determining its effectiveness. However, disentangling these two contributions is a challenge for both experiments and simulations. In this work, we have systematically investigated the ice-nucleating ability of the very same compound, cholesterol, from the crystalline (and thus ordered) form to disordered self-assembled monolayers. Leveraging a combination of experiments and simulations, we identify a “sweet spot” in terms of the surface coverage of the monolayers, whereby cholesterol maximises its ability to nucleate ice (which remains inferior to that of crystalline cholesterol) by enhancing the structural order of the interfacial water molecules. These findings have practical implications for the rational design of synthetic ice-nucleating agents.

The freezing of water into ice is still not fully understood. Here, we investigate the role of structural disorder within the biologically relevant impurities that facilitate this fundamental phase transition.

Lipid bilayers as potential ice nucleating agents

Cellular damage is a key issue in the context of cryopreservation. Much of this damage is believed to be caused by extracellular ice formation at temperatures well above the homogeneous freezing point of pure water. Hence the question: what initiates ice nucleation during cryopreservation? In this paper, we assess whether cellular membranes could be responsible for facilitating the ice nucleation process, and what characteristics would make them good or bad ice nucleating agents. By means of molecular dynamics simulations, we investigate a number of phospholipids and lipopolysaccharide bilayers at the interface with supercooled liquid water. While these systems certainly appear to act as ice nucleating agents, it is likely that other impurities might also play a role in initiating extracellular ice nucleation. Furthermore, we elucidate the factors which affect a bilayer's ability to act as an ice nucleating agent; these are complex, with specific reference to both chemical and structural factors. These findings represent a first attempt to pinpoint the origin of extracellular ice nucleation, with important implications for the cryopreservation process.

The atomistic details of the ice recrystallisation inhibition activity of PVA

Understanding the ice recrystallisation inhibition (IRI) activity of antifreeze biomimetics is crucial to the development of the next generation of cryoprotectants. In this work, we bring together molecular dynamics simulations and quantitative experimental measurements to unravel the microscopic origins of the IRI activity of poly(vinyl)alcohol (PVA)-the most potent of biomimetic IRI agents. Contrary to the emerging consensus, we find that PVA does not require a "lattice matching" to ice in order to display IRI activity: instead, it is the effective volume of PVA and its contact area with the ice surface which dictates its IRI strength. We also find that entropic contributions may play a role in the ice-PVA interaction and we demonstrate that small block co-polymers (up to now thought to be IRI-inactive) might display significant IRI potential. This work clarifies the atomistic details of the IRI activity of PVA and provides novel guidelines for the rational design of cryoprotectants.

Influence of the dimensionality of the periodic boundary conditions on the transport of a drug-peptide complex across model cell membranes

Many research efforts are devoted to improving the efficiency of chemotherapy. One of the aspects is to facilitate the transport of drugs across the cell membranes by attaching the therapeutics to a carrier molecule. The current study focuses on computational investigation of such a system with doxorubicin as the model drug, which is covalently bound to a cell-penetrating peptide. The correct description of its membrane translocation at the molecular level requires proper choice of the model membrane and of the simulation parameters. For the purpose, two phospholipid bilayers are built, one containing solely DPPC and another with mixed lipid content mimicking the composition of a human erythrocyte membrane. Atomistic molecular dynamics simulations are carried out in two types of periodic boundary conditions (2D and 3D PBC), in order to assess the effect of the periodicity dimensionality on the intermolecular interactions. The evolution of some basic characteristics of the bilayers and of the drug-peptide complex is tracked: mass density profiles, electrostatic potentials, lateral diffusion coefficients and areas per lipid, lipid-complex radial distribution functions, secondary structure of the peptide and orientation of the drug relative to the membrane. Thus, the influence of the periodic boundary conditions is quantified and it shows that the mixed system in 3D PBC is the most suitable for analysis of the translocation of the transporting moiety across cell membranes.

Molecular Investigation of Contact Line Movement in Electrowetted Nanodroplets

Molecular dynamics (MD) simulation of an electrowetted nanodroplet is performed to understand the fundamental origin of the involved parameters resulted from the molecular movement in the vicinity of the three-phase contact line (TPCL). During the spreading of the droplet, contact line friction (CLF) force is found to be the controlling one among all other resistive forces. Being molecular in nature, MD study is required to unveil the CLF, which is manifested by the TPCL friction coefficient ζ. The combined effect of temperature, electric field, and surface wettability, manifested by the solid-liquid Lennard-Jones interaction parameter, is studied to explore the droplet spreading. The entire droplet wetting dynamics is divided into two different regimes, namely, spreading regime and equilibrium regime. The molecular frequency during the TPCL movement in the equilibrium regime is affected by the presence of any external perturbation and results in an alteration of ζ. The predetermined knowledge of the alteration of CLF due to the coupling effect of electric field and temperature will have a potential application towards designing electric field-inspired droplet movement devices.

Rheology of water in small nanotubes

The properties of water in confinement are very different from those under bulk conditions. In some cases the melting point of ice may be shifted and one may find either ice, icelike water, or a state in which freezing is completely inhibited. Understanding the dynamics and rheology of water in confined media, such as small nanotubes, is of fundamental importance to the biological properties of micro-organisms at low temperatures, to the development of new devices for preserving DNA samples, and for other biological materials and fluids, lubrication, and development of nanostructured materials. We study rheology and dynamics of water in small nanotubes using extensive equilibrium and nonequilibrium molecular dynamics simulations. The results demonstrate that in strong confinement in nanotubes at temperatures significantly below and above bulk freezing temperature water behaves as a shear-thinning fluid at shear rates smaller than the inverse of the relaxation time in the confined medium. In addition, our results indicate the presence of regions in which the local density of water varies significantly over the same range of temperature in the nanotube. These findings may also have important implications for the design of nanofluidic systems.

Cosolvent Impurities in SWCNT Nanochannel Confinement: Length Dependence of Water Dynamics Investigated with Atomistic Simulations

The advent of nanotechnology has seen a growing interest in the nature of fluid flow and transport under nanoconfinement. The present study leverages fully atomistic molecular dynamics (MD) simulations to study the effect of nanochannel length and intrusion of molecules of the organic solvent, hexafluoro-2-propanol (HFIP), on the dynamical characteristics of water within it. Favorable interactions of HFIP with the nanochannels comprised of single-walled carbon nanotubes traps them over time scales greater than 100 ns, and confinement confers small but distinguishable spatial redistribution between neighboring HFIP pairs. Water molecules within the nanochannels show clear signatures of dynamical slowdown relative to bulk water even for pure systems. The presence of HFIP causes further rotational and translational slowdown in waters when the nanochannel dimension falls below a critical length of 30 Å. The enhanced slowdown in the presence of HFIP is quantified from characteristic relaxation parameters and diffusion coefficients in the absence and presence of HFIP. It is finally seen that the net flow of water between the ends of the nanochannel shows a decreasing dependence with nanochannel length only when the number of HFIP molecules is small. These results lend insights into devising ways of modulating solvent properties within nanochannels with cosolvent impurities.

Discrete and Continuum Models for the Salt in Crowded Environments of Suspended Charged Particles

Electrostatic forces greatly affect the overall dynamics and diffusional activities of suspended charged particles in crowded environments. Accordingly, the concentration of counter- or co-ions in a fluid-''the salt"-determines the range, strength, and order of electrostatic interactions between particles. This environment fosters engineering routes for controlling directed assembly of particles at both the micro- and nanoscale. Here, we analyzed two computational modeling schemes that considered salt within suspensions of charged particles, or polyelectrolytes: discrete and continuum. Electrostatic interactions were included through a Green's function formalism, where the confined fundamental solution for Poisson's equation is resolved by the general geometry Ewald-like method. For the discrete model, the salt was considered as regularized point-charges with a specific valence and size, while concentration fields were defined for each ionic species for the continuum model. These considerations were evolved using Brownian dynamics of the suspended charged particles and the discrete salt ions, while a convection-diffusion transport equation, including the Nernst-Planck diffusion mechanism, accounted for the dynamics of the concentration fields. The salt/particle models were considered as suspensions under slit-confinement conditions for creating crowded "macro-ions", where density distributions and radial distribution functions were used to compare and differentiate computational models. Importantly, our analysis shows that disparate length scales or increased system size presented by the salt and suspended particles are best dealt with using concentration fields to model the ions. These findings were then validated by novel simulations of a semipermeable polyelectrolyte membrane, at the mesoscale, from which ionic channels emerged and enable ion conduction.

Complex Behavior of Ordered and Icelike Water in Carbon Nanotubes near Its Bulk Boiling Point

We report the results of extensive molecular dynamics (MD) simulation of water in a carbon nanotube (CNT) with a specific diameter over a wide range of temperatures from 343 to 423 K. In order to characterize the nature of water, we have computed the Kirkwood g-factor, the ten Wolde parameter, the radial distribution, the cage correlation, the intermediate scattering functions, the mean-square displacements of the water molecules, and the connectivity of the oxygen atoms. The computed properties provide evidence for complex behavior. Some of the properties indicate an icelike structure, while others point to ordered (but not necessarily frozen) water. The connectivity is close to 9. The ordered water exists both below and above its bulk boiling point. The order is identified based on the ten Wolde parameter and may explain, along with the dynamic slow down, the recent discovery of "ice" in CNTs near the bulk boiling point in a certain range of CNT diameters, not seen in tubes of other sizes.

Studying Kv Channels Function using Computational Methods

In recent years, molecular modeling techniques, combined with MD simulations, provided significant insights on voltage-gated (Kv) potassium channels intrinsic properties. Among the success stories are the highlight of molecular level details of the effects of mutations, the unraveling of several metastable intermediate states, and the influence of a particular lipid, PIP₂, in the stability and the modulation of Kv channel function. These computational studies offered a detailed view that could not have been reached through experimental studies alone. With the increase of cross disciplinary studies, numerous experiments provided validation of these computational results, which endows an increase in the reliability of molecular modeling for the study of Kv channels. This chapter offers a description of the main techniques used to model Kv channels at the atomistic level.

Atomistic Molecular Dynamics Simulations of Crude Oil/Brine Displacement in Calcite Mesopores

Unconventional reservoirs such as hydrocarbon-bearing shale formations and ultratight carbonates generate a large fraction of oil and gas production in North America. The characteristic feature of these reservoirs is their nanoscale porosity that provides significant surface areas between the pore walls and the occupying fluids. To better assess hydrocarbon recovery from these formations, it is crucial to develop an improved insight into the effects of wall-fluid interactions on the interfacial phenomena in these nanoscale confinements. One of the important properties that controls the displacement of fluids inside the pores is the threshold capillary pressure. In this study, we present the results of an integrated series of large-scale molecular dynamics (MD) simulations performed to investigate the effects of wall-fluid interactions on the threshold capillary pressures of oil-water/brine displacements in a calcite nanopore with a square cross section. Fully atomistic models are utilized to represent crude oil, brine, and calcite in order to accommodate electrostatic interactions and H-bonding between the polar molecules and the calcite surface. To this end, we create mixtures of various polar and nonpolar organic molecules to better represent the crude oil. The interfacial tension between oil and water/brine and their contact angle on calcite surface are simulated. We study the effects of oil composition, water salinity, and temperature and pressure conditions on these properties. The threshold capillary pressure values are also obtained from the MD simulations for the calcite nanopore. We then compare the MD results against those generated using the Mayer-Stowe-Princen (MSP) method and explain the differences.

Multi-Level Ewald: A hybrid multigrid / Fast Fourier Transform approach to the electrostatic particle-mesh problem

We present a new method for decomposing the one convolution required by standard Particle-Particle Particle-Mesh (P(3)M) electrostatic methods into a series of convolutions over slab-shaped subregions of the original simulation cell. Most of the convolutions derive data from separate regions of the cell and can thus be computed independently via FFTs, in some cases with a small amount of zero padding so that the results of these sub-problems may be reunited with minimal error. A single convolution over the entire cell is also performed, but using a much coarser mesh than the original problem would have required. This "Multi-Level Ewald" (MLE) method therefore requires moderately more FFT work plus the tasks of interpolating between different sizes of mesh and accumulating the results from neighboring sub-problems, but we show that the added expense can be less than 10% of the total simulation cost. We implement MLE as an approximation to the Smooth Particle Mesh Ewald (SPME) style of P(3)M, and identify a number of tunable parameters in MLE. With reasonable settings pertaining to the degree of overlap between the various sub-problems and the accuracy of interpolation between meshes, the errors obtained by MLE can be smaller than those obtained in molecular simulations with typical SPME settings. We compare simulations of a box of water molecules performed with MLE and SPME, and show that the energy conservation, structural, and dynamical properties of the system are more affected by the accuracy of the SPME calculation itself than by the additional MLE approximation. We anticipate that the MLE method's ability to break a single convolution into many independent sub-problems will be useful for extending the parallel scaling of molecular simulations.

Interfacial tension does not drive asymmetric nanoscale electrowetting on graphene

We report molecular dynamics simulations of the electrowetting behavior of liquids in confinement between two oppositely charged graphene sheets. We observe that changes in the static contact angles of water, salty (4 M NaCl) water, and 1-butyl-3-methylimidazolium tetrafluoroborate ([bmim][BF4]) (a room temperature ionic liquid) exhibit an asymmetric dependence on electric field polarity. The solid-liquid interfacial tension, which is expected to drive these changes, has been calculated independently by integrating the reversible work performed upon introducing positive and negative surface charges. This quantity shows either no dependence on the polarity of the electric field (water) or a dependence exactly opposite to the one obtained by applying the Young-Lippmann equation to the observed contact angles ([bmim][BF4]). Our analysis indicates that the observed contact angle asymmetry finds its origin in the liquid structure in the vicinity of the three-phase contact line. In particular, it is suggested that the molecular orientation properties are crucial to determine the asymmetric wetting behavior of pure water; in addition, the contrast in the strength of the ion hydration shells has a decisive influence on the NaCl solution behavior.

Electric field-driven water dipoles: nanoscale architecture of electroporation

Electroporation is the formation of permeabilizing structures in the cell membrane under the influence of an externally imposed electric field. The resulting increased permeability of the membrane enables a wide range of biological applications, including the delivery of normally excluded substances into cells. While electroporation is used extensively in biology, biotechnology, and medicine, its molecular mechanism is not well understood. This lack of knowledge limits the ability to control and fine-tune the process. In this article we propose a novel molecular mechanism for the electroporation of a lipid bilayer based on energetics analysis. Using molecular dynamics simulations we demonstrate that pore formation is driven by the reorganization of the interfacial water molecules. Our energetics analysis and comparisons of simulations with and without the lipid bilayer show that the process of poration is driven by field-induced reorganization of water dipoles at the water-lipid or water-vacuum interfaces into more energetically favorable configurations, with their molecular dipoles oriented in the external field. Although the contributing role of water in electroporation has been noted previously, here we propose that interfacial water molecules are the main players in the process, its initiators and drivers. The role of the lipid layer, to a first-order approximation, is then reduced to a relatively passive barrier. This new view of electroporation simplifies the study of the problem, and opens up new opportunities in both theoretical modeling of the process and experimental research to better control or to use it in new, innovative ways.

Modeling complex biological systems: From solution chemistry to membranes and channels

Complex biological systems are intimately linked to their environment, a very crowded and equally complex solution compartmentalized by fluid membranes. Modeling such systems remains challenging and requires a suitable representation of these solutions and their interfaces. Here, we focus on particle-based modeling at an atomistic level using molecular dynamics (MD) simulations. As an example, we discuss important steps in modeling the solution chemistry of an ion channel of the ligand-gated ion channel receptor family, a major target of many drugs including anesthetics and addiction treatments. The bacterial pentameric ligand-gated ion channel (pLGIC) called GLIC provides clues about the functional importance of solvation, in particular for mechanisms such as permeation and gating. We present some current challenges along with promising novel modeling approaches.

Molecular dynamics simulations of voltage-gated cation channels: insights on voltage-sensor domain function and modulation

Since their discovery in the 1950s, the structure and function of voltage-gated cation channels (VGCC) has been largely understood thanks to results stemming from electrophysiology, pharmacology, spectroscopy, and structural biology. Over the past decade, computational methods such as molecular dynamics (MD) simulations have also contributed, providing molecular level information that can be tested against experimental results, thereby allowing the validation of the models and protocols. Importantly, MD can shed light on elements of VGCC function that cannot be easily accessed through “classical” experiments. Here, we review the results of recent MD simulations addressing key questions that pertain to the function and modulation of the VGCC’s voltage-sensor domain (VSD) highlighting: (1) the movement of the S4-helix basic residues during channel activation, articulating how the electrical driving force acts upon them; (2) the nature of the VSD intermediate states on transitioning between open and closed states of the VGCC; and (3) the molecular level effects on the VSD arising from mutations of specific S4 positively charged residues involved in certain genetic diseases.

Development of molecular simulation methods to accurately represent protein-surface interactions: Method assessment for the calculation of electrostatic effects

The simulation of the interactions of proteins with charged surfaces in a condensed-phase aqueous solution containing electrolytes using empirical force field based methods is predominantly governed by nonbonded interactions between the atoms of the protein, surface, and the solvent. Electrostatic effects represent the strongest type of these interactions and the type that is most difficult to accurately represent because of their long-range influence. While many different methods have been developed to represent electrostatic interactions, the particle mesh Ewald summation (PME) method is generally considered to be the most accurate one for calculating these effects. However, the PME method was designed for systems with three-dimensional (3D) periodicity, and not for interfacial systems such as the case of protein adsorption to a charged surface. Interfacial systems such as these have only two-dimensional periodicity, which may not be appropriate for treatment with PME due to the possibility that the presence of multiple charged image surfaces parallel to the primary simulation cell's surface, may introduce nonphysical effects on the behavior of the charged molecules in the system. In an effort to address this issue, the authors have conducted a set of nanosecond-scale molecular dynamics simulations to calculate the equilibrium distribution of Na(+) and Cl(-) ions near a charged surface using PME and a range of radial cutoff methods for treating electrostatic interactions, where the cutoffs prevent interaction with the periodic images of the system. The resulting ion concentration profiles were compared to one another and to a continuum analytical solution of the theoretical ion distribution obtained from the Poisson-Boltzmann equation. Their results show that the PME method does not introduce the suspected nonphysical effects in the ion distributions due to the 3D periodic images of the system, thus indicating that it is appropriate for use for this type of molecular simulation. Although their interest is motivated by protein-surface interactions, the conclusions are applicable for the treatment of electrostatics in other aqueous systems with two-dimensional periodicity.

Calculation of the electrostatic potential of lipid bilayers from molecular dynamics simulations: methodological issues

The electrostatic properties of lipid membranes are of profound importance as they are directly associated with membrane potential and, consequently, with numerous membrane-mediated biological phenomena. Here we address a number of methodological issues related to the computation of the electrostatic potential from atomic-scale molecular dynamics simulations of lipid bilayers. We discuss two slightly different forms of Poisson equation that are normally used to calculate the membrane potential: (i) a classical form when the potential and the electric field are chosen to be zero on one of the sides of a simulation box and (ii) an alternative form, when the potential is set to be the same on the opposite sides of a simulation box. Both forms differ by a position-dependent correction term, which has been shown to be proportional to the overall dipole moment of a bilayer system (for neutral systems). For symmetric bilayers we demonstrate that both approaches give essentially the same potential profiles, provided that simulations are long enough (a production run of at least 100 ns is required) and that fluctuations of the center of mass of a bilayer are properly accounted for. In contrast, for asymmetric lipid bilayers, the second approach is no longer appropriate due to a nonzero net dipole moment across a simulation box with a single asymmetric bilayer. We demonstrate that in this case the electrostatic potential can adequately be described by the classical form of Poisson equation, provided that it is employed in conjunction with tin-foil boundary conditions, which exactly balance a nonzero surface charge of a periodically replicated multibilayer system. Furthermore, we show that vacuum boundary conditions give qualitatively similar potential profiles for asymmetric lipid bilayers as compared to the conventional periodic boundaries, but accurate determination of the transmembrane potential difference is then hindered due to detachment of some water dipoles from bulk aqueous solution to vacuum.

Effect of induced electric field on single-file reverse osmosis

We investigated the effect of the electric field on single-file reverse osmosis (RO) water flux using molecular dynamics simulations. The electric field is generated by introducing oppositely charged biomolecules to the salt solution and pure water chambers attached to the nanopore. Simulation results indicate that an electric field in the direction of RO enhances the water flux while in the direction opposite to RO it suppresses the water flux. When the RO water flux is enhanced, the single-file water dipoles are aligned in the direction of the electric field. The addition of an electric field in the direction of RO led to a flux of 3 water molecules ns(-1) by constantly maintaining water dipole vectors in the direction of the electric field, and this water flux is superimposed on the pressure driven water flux.

Langmuir monolayers of a hydrogenated/fluorinated catanionic surfactant: from the macroscopic to the nanoscopic size scale

Langmuir monolayers of the hydrogenated/fluorinated catanionic surfactant cetyltrimethylammonium perfluorooctanoate at the air/water interface are studied at room temperature. Excess Gibbs energies of mixing, DeltaG(E), as well as transition areas and pressures, were obtained from the surface pressure-area isotherm. The DeltaG(E) curve indicates that tail-tail interactions are more important than head-head interactions at low pressures and vice versa. Atomic force microscopy and molecular dynamics simulations allowed a fine characterization of the monolayer structure as a function of the area per molecule at mesoscopic and nanoscopic size scales, respectively. A combined analysis of the techniques allow us to conclude that electrostatic interactions between the ionic head groups are dominant in the monolayer while hydrophobic parts are of secondary importance. Overall, results obtained from the different techniques complement to each other, giving a comprehensive characterization of the monolayer.

A structural model of the pore-forming region of the skeletal muscle ryanodine receptor (RyR1)

Ryanodine receptors (RyRs) are ion channels that regulate muscle contraction by releasing calcium ions from intracellular stores into the cytoplasm. Mutations in skeletal muscle RyR (RyR1) give rise to congenital diseases such as central core disease. The absence of high-resolution structures of RyR1 has limited our understanding of channel function and disease mechanisms at the molecular level. Here, we report a structural model of the pore-forming region of RyR1. Molecular dynamics simulations show high ion binding to putative pore residues D4899, E4900, D4938, and D4945, which are experimentally known to be critical for channel conductance and selectivity. We also observe preferential localization of Ca(2+) over K(+) in the selectivity filter of RyR1. Simulations of RyR1-D4899Q mutant show a loss of preference to Ca(2+) in the selectivity filter as seen experimentally. Electrophysiological experiments on a central core disease mutant, RyR1-G4898R, show constitutively open channels that conduct K(+) but not Ca(2+). Our simulations with G4898R likewise show a decrease in the preference of Ca(2+) over K(+) in the selectivity filter. Together, the computational and experimental results shed light on ion conductance and selectivity of RyR1 at an atomistic level.

Water-mediated ordering of nanoparticles in an electric field

Interfacial polar molecules feature a strongly anisotropic response to applied electric field, favoring dipole orientations parallel to the interface. In water, in particular, this effect combines with generic orientational preferences induced by spatial asymmetry of water hydrogen bonding under confined geometry, which may give rise to a Janus interface. The two effects manifest themselves in considerable dependence of water polarization on both the field direction relative to the interface and the polarity (sign) of the field. Using molecular simulations, we demonstrate strong field-induced orientational forces acting on apolar surfaces through water mediation. At a field strength comparable to electric fields around a DNA polyion, the torques we predict to act on an adjacent nanoparticle are sufficient to overcome thermal fluctuations. These torques can align a particle with surface as small as 1 nm2. The mechanism can support electrically controlled ordering of suspended nanoparticles as a means of tuning their properties and can find application in electro-nanomechanical devices.

Modeling and molecular dynamics simulation of the human gonadotropin-releasing hormone receptor in a lipid bilayer

In the present study, a model for the human gonadotropin-releasing hormone receptor embedded in an explicit lipid bilayer was developed. The final conformation was obtained by extensive molecular dynamics simulations of a homology model based on the bovine rhodopsin crystal structure. The analysis of the receptor structure allowed us to detect a number of specific contacts between different amino acid residues, as well as water- and lipid-mediated interactions. These interactions were stable in six additional independent 35 ns long simulations at 310 and 323 K, which used the refined model as the starting structure. All loops, particularly the extracellular loop 2 and the intracellular loop 3, exhibited high fluctuations, whereas the transmembrane helices were more static. Although other models of this receptor have been previously developed, none of them have been subjected to extensive molecular dynamics simulations, and no other three-dimensional structure is publicly available. Our results suggest that the presence of ions as well as explicit solvent and lipid molecules are critical for the structure of membrane protein models, and that molecular dynamics simulations are certainly useful for their refinement.

Membrane potential and electrostatics of phospholipid bilayers with asymmetric transmembrane distribution of anionic lipids

It is well-established that native plasma membranes are characterized by an asymmetric distribution of charged (anionic) lipids across the membrane. To clarify how the asymmetry can affect membrane electrostatics, we have performed extensive atomic-scale molecular dynamics simulations of asymmetric lipid membranes composed of zwitterionic (phosphatidylcholine (PC) or phosphatidylethanolamine (PE)) and anionic (phosphatidylserine (PS)) leaflets. It turns out that the asymmetry in transmembrane distribution of anionic lipids gives rise to a nonzero potential difference between the two sides of the membrane. This potential arises from the difference in surface charges of the two leaflets. The magnitude of the intrinsic membrane potential was found to be 238 mV and 198 mV for PS/PC and PS/PE membranes, respectively. Remarkably, this potential is of the same sign as the membrane potential in cells. Our findings, being in reasonable agreement with available experimental data, lend support to the idea that the transmembrane lipid asymmetry typical of most living cells contributes to the membrane potential.

Energetics of divalent selectivity in a calcium channel: the ryanodine receptor case study

A model of the ryanodine receptor (RyR) calcium channel is used to study the energetics of binding selectivity of Ca(2+) versus monovalent cations. RyR is a calcium-selective channel with a DDDD locus in the selectivity filter, similar to the EEEE locus of the L-type calcium channel. While the affinity of RyR for Ca(2+) is in the millimolar range (as opposed to the micromolar range of the L-type channel), the ease of single-channel measurements compared to L-type and its similar selectivity filter make RyR an excellent candidate for studying calcium selectivity. A Poisson-Nernst-Planck/density functional theory model of RyR is used to calculate the energetics of selectivity. Ca(2+) versus monovalent selectivity is driven by the charge/space competition mechanism in which selectivity arises from a balance of electrostatics and the excluded volume of ions in the crowded selectivity filter. While electrostatic terms dominate the selectivity, the much smaller excluded-volume term also plays a substantial role. In the D4899N and D4938N mutations of RyR that are analyzed, substantial changes in specific components of the chemical potential profiles are found far from the mutation site. These changes result in the significant reduction of Ca(2+) selectivity found in both theory and experiments.

Generalized gradient-augmented harmonic Fourier beads method with multiple atomic and/or center-of-mass positional restraints

We describe a generalization of the gradient-augmented harmonic Fourier beads method for finding minimum free-energy transition path ensembles and similarly minimum potential energy paths to allow positional restraints on the centers of mass of selected atoms. The generalized gradient-augmented harmonic Fourier beads (ggaHFB) method further extends the scope of the HFB methodology to studying molecule transport across various mobile phases such as lipid membranes. Furthermore, the new implementation improves the applicability of the HFB method to studies of ligand binding, protein folding, and enzyme catalysis as well as modeling equilibrium pulling experiments. Like its predecessor, the ggaHFB method provides accurate energy profiles along the specified paths and in certain simple cases avoids the need for path optimization. The utility of the ggaHFB method is demonstrated with an application to the water permeation through a single-wall (5,5) carbon nanotube with a diameter of 6.78 A and length of 16.0 A. We provide a simple rationale as to why water enters the hydrophobic nanotube and why it does so in pulses and in wire assembly.

Molecular dynamics simulations of potassium channels

Despite the complexity of ion-channels, MD simulations based on realistic all-atom models have become a powerful technique for providing accurate descriptions of the structure and dynamics of these systems, complementing and reinforcing experimental work. Successful multidisciplinary collaborations, progress in the experimental determination of three-dimensional structures of membrane proteins together with new algorithms for molecular simulations and the increasing speed and availability of supercomputers, have made possible a considerable progress in this area of biophysics. This review aims at highlighting some of the work in the area of potassium channels and molecular dynamics simulations where numerous fundamental questions about the structure, function, folding and dynamics of these systems remain as yet unresolved challenges.

Direct computer simulation of water-mediated force between supported phospholipid membranes

The grand canonical Monte Carlo technique is used to calculate the water-mediated force operating between two supported 1,2-dilauroyl-DL-phosphatidylethanolamine (DLPE) membranes in the short separation range. The intra- and intermolecular interactions in the system are described with a combination of an AMBER-based force field for DLPE and a TIP4P model for water. The long range contributions to the electrostatic interaction energy are treated in the dipole-dipole group-based approximation. The total water-mediated force is analyzed in terms of its hydration component and the component due to the direct interaction between the membranes. The latter is, in addition, partitioned into the electrostatic, van der Waals, and steric repulsion contributions to give an idea of their relative significance in the water-mediated interaction of the membranes.

Deprotonation by dehydration: the origin of ammonium sensing in the AmtB channel

The AmtB channel passively allows the transport of NH₄⁺ across the membranes of bacteria via a “gas” NH₃ intermediate and is related by homology (sequentially, structurally, and functionally) to many forms of Rh protein (both erythroid and nonerythroid) found in animals and humans. New structural information on this channel has inspired computational studies aimed at clarifying various aspects of NH₄⁺ recruitment and binding in the periplasm, as well as its deprotonation. However, precise mechanisms for these events are still unknown, and, so far, explanations for subsequent NH₃ translocation and reprotonation at the cytoplasmic end of the channel have not been rigorously addressed. We employ molecular dynamics simulations and free energy methods on a full AmtB trimer system in membrane and bathed in electrolyte. Combining the potential of mean force for NH₄⁺/NH₃ translocation with data from thermodynamic integration calculations allows us to find the apparent pK_a of NH₄⁺ as a function of the transport axis. Our calculations reveal the specific sites at which its deprotonation (at the periplasmic end) and reprotonation (at the cytoplasmic end) occurs. Contrary to most hypotheses, which ascribe a proton-accepting role to various periplasmic or luminal residues of the channel, our results suggest that the most plausible proton donor/acceptor at either of these sites is water. Free-energetic analysis not only verifies crystallographically determined binding sites for NH₄⁺ and NH₃ along the transport axis, but also reveals a previously undetermined binding site for NH₄⁺ at the cytoplasmic end of the channel. Analysis of dynamics and the free energies of all possible loading states for NH₃ inside the channel also reveal that hydrophobic pressure and the free-energetic profile provided by the pore lumen drives this species toward the cytoplasm for protonation just before reaching the newly discovered site.

Selective flow of ammonium manifests itself in a unique way in the case of the ammonium channel, AmtB, allowing it to interact closely with cytoplasmic signal transduction proteins in order to “sense” the presence of extracellular ammonium. Although it is well known that AmtB transports ammonia (NH₃) rather than ammonium ion (NH₄⁺), it is unclear from the channel's atomic structure exactly where and how, along its pathway toward the cytoplasm, NH₄⁺ becomes deprotonated to form NH₃, and reprotonated on the cytoplasmic end of the channel to form NH₄⁺ to enter the cell. We use a combination of molecular dynamics simulation techniques to glean the thermodynamics associated with these key events in ammonium translocation. Our findings provide a novel perspective on how this family of channels indirectly controls ammonium protonation—by directly controlling its hydration. Such a perspective should lend new insight to interpretations of experimental data, and could possibly lead to new strategies in an envisioned future for the design of nanopores that can control the protonated state of permeant species.

A molecular dynamics analysis of the GCC-box binding domain in ethylene-responsive element binding factors

Ethylene-responsive element (ERE) binding factors is responsible for a consensus nucleotide sequence AGCCGCC (GCC-box) binding in many important process of plant growing through gene regulation and mediating signal transduction pathways in response to environmental stress. The GCC-box binding domain (GBD) as a novel fold for DNA recognition has been analyzed by means of molecular dynamics. The simulations show that the complex of GBD-DNA trajectories show similar fluctuations in the atomic positions as uncomplexed, particularly at three beta strands involving DNA binding. The calculations of entropy also affirm that GBD flexibility is basically similar for two ligation states. Further, the two complexation states present similar patterns of concerted motions, indicating that the bound DNA cannot alter GBD flexibility. It is inferred that the flexibility of GBD molecule is independent of its ligation state. So in the protein-DNA recognition, the GBD cannot be easily induced while DNA shows better flexibility. Comparison between simulations of unligated GBD and the complexed GBD (in isolation or DNA-bound) reveals intrinsic flexibilities in some certain parts of the molecule play a key role in DNA recognition. In addition, MD simulation identifies that water molecule may mediate interaction between GBD and DNA.

Transmembrane Helix−Helix Interactions: Comparative Simulations of the Glycophorin A Dimer

The glycophorin helix dimer is a paradigm for the exploration of helix-helix interactions in integral membrane proteins. Two NMR structures of the dimer are known, one in a detergent micelle and one in a lipid bilayer. Multiple (4 x 50 ns) molecular dynamics simulations starting from each of the two NMR structures, with each structure in either a dodecyl phosphocholine (DPC) micelle or a dimyristoyl phosphatidylcholine (DMPC) bilayer, have been used to explore the conformational dynamics of the helix dimer. Analysis of the helix-helix interaction, mediated by the GxxxG sequence motif, suggests convergence of the simulations to a common model. This is closer to the NMR structure determined in a bilayer than to micelle structure. The stable dimer interface in the final simulation model is characterized by (i) Gly/Gly packing and (ii) Thr/Thr interhelix H-bonds. These results demonstrate the ability of extended molecular dynamics simulations in a lipid bilayer environment to refine membrane protein structures or models derived from experimental data obtained in protein/detergent micelles.

Steered Molecular Dynamics Simulations of Na+ Permeation across the Gramicidin A Channel

The potential of mean forces (PMF) governing Na+ permeation through gramicidin A (gA) channels with explicit water and membrane was characterized using steered molecular dynamics (SMD) simulations. Constant-force SMD with a steering force parallel to the channel axis revealed at least seven energy wells in each monomer of the channel dimer. Except at the channel dimer interface, each energy well is associated with at least three and at most four backbone carbonyl oxygens and two water oxygens in a pseudo-hexahedral or pseudo-octahedral coordination with the Na+ ion. Repeated constant-velocity SMD by dragging a Na+ ion from each energy well in opposite directions parallel to the channel axis allowed the computation of the PMF across the gA channel, revealing a global minimum corresponding to Na+ binding sites near the entrance of gA at +/-9.3 A from the geometric center of the channel. The effect of volatile anesthetics on the PMF was also analyzed in the presence of halothane molecules. Although the accuracy of the current PMF calculation from SMD simulations is not yet sufficient to quantify the PMF difference with and without anesthetics, the comparison of the overall PMF profiles nevertheless confirms that the anesthetics cause insignificant changes to the structural makeup of the free energy wells along the channel and the overall permeation barrier. On average, the PMF appears less rugged in the outer part of the channel in the presence of anesthetics, consistent with our earlier finding that halothane interaction with anchoring residues makes the gA channel more dynamic. A causal relationship was observed between the reorientation of the coordinating backbone carbonyl oxygen and Na+ transit from one energy well to another, suggesting the possibility that even minute changes in the conformation of pore-lining residues due to dynamic motion could be sufficient to trigger the ion permeation. Because some of the carbonyl oxygens contribute to Na+ coordination in two adjacent energy wells, our SMD results reveal that the atomic picture of ion "hopping" through a gA channel actually involves a Na+ ion being carried in a relay by the coordinating oxygens from one energy well to the next. Steered molecular dynamics complements other computational approaches as an attractive means for the atomistic interpretation of experimental permeation studies.

Voltage-dependent hydration and conduction properties of the hydrophobic pore of the mechanosensitive channel of small conductance

A detailed picture of water and ion properties in small pores is important for understanding the behavior of biological ion channels. Several recent modeling studies have shown that small, hydrophobic pores exclude water and ions even if they are physically large enough to accommodate them, a mechanism called hydrophobic gating. This mechanism has been implicated in the gating of several channels, including the mechanosensitive channel of small conductance (MscS). Although the pore in the crystal structure of MscS is wide and was initially hypothesized to be open, it is lined by hydrophobic residues and may represent a nonconducting state. Molecular dynamics simulations were performed on MscS to determine whether or not the structure can conduct ions. Unlike previous simulations of hydrophobic nanopores, electric fields were applied to this system to model the transmembrane potential, which proved to be important. Although simulations without a potential resulted in a dehydrated, occluded pore, the application of a potential increased the hydration of the pore and resulted in current flow through the channel. The calculated channel conductance was in good agreement with experiment. Therefore, it is likely that the MscS crystal structure is closer to a conducting than a nonconducting state.

Molecular dynamics simulation approaches to K channels: conformational flexibility and physiological function

Molecular modeling and simulations enable extrapolation for the structure of bacterial potassium channels to the function of their mammalian homologues. Molecular dynamics simulations have revealed the concerted single-file motion of potassium ions and water molecules through the selectivity filter of K channels and the role of filter flexibility in ion permeation and in "fast gating." Principal components analysis of extended K channel simulations suggests that hinge-bending of pore-lining M2 (or S6) helices plays a key role in K channel gating. Based on these and other simulations, a molecular model for gating of inward rectifier K channel gating is presented.